Cooldowns do change the balance of the game, but for the better, and with more balancing options.
If you want to keep the spells (as in their actual effects) mostly intact (vs. the 5e rules), then this is the very opposite of truth. 5e classes/actions/spells are decently (though not perfectly) balanced around the rest mechanics, in both P&P and cRPGs - as long as you implement 5e rules relatively faithfully (Solasta...).
If you want to throw the rules completely out of the window (again, actual licensing issues might arise, not sure about WotC's position on this) and reimplement/rebalance all actions/spells, then depending on the quality of your implementation, the balance may end up being worse or better.
And sure, the more moddable the game is, the better.
